The notion of "cases" or "instances" depends upon propositional functions. Consider, for example, the kind of process suggested by what is called "generalisation," and let us take some very primitive example, say, "lightning is followed by thunder." We have a number of "instances" of this, i.e. a number of propositions such as: "this is a flash of lightning and is followed by thunder." What are these occurrences "instances" of? They are instances of the propositional function: "If is a flash of lightning, is followed by thunder." The process of generalisation (with whose validity we are fortunately [Pg 156] not concerned) consists in passing from a number of such instances to the universal truth of the propositional function: "If is a flash of lightning, is followed by thunder." It will be found that, in an analogous way, propositional functions are always involved whenever we talk of instances or cases or examples. We do not need to ask, or attempt to answer, the question: "What is a propositional function?" A propositional function standing all alone may be taken to be a mere schema, a mere shell, an empty receptacle for meaning, not something already significant. We are concerned with propositional functions, broadly speaking, in two ways: first, as involved in the notions "true in all cases" and "true in some cases"; secondly, as involved in the theory of classes and relations. The second of these topics we will postpone to a later chapter; the first must occupy us now.